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Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

Quantitative Aptitude for Banking Preparation

UPSC : Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

The document Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev is a part of the UPSC Course Quantitative Aptitude for Banking Preparation.

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Areas

Areas of some well-known figures are given below:

Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

Ex.1 A horizontal pipe for carrying floodwater
has diameter 1 m. When water in it is 10 cm
deep then the width of water surface AB is equal
to ________ cm.

Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev
(1) 10 cm

(2) 25 cm
(3) 60 cm

(4) 70 cm
(5) None

Sol.

Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

Let O be the centre of circle.
In ΔOAD
502 = 402 + x2
2500 – 1600 = x²
x² = 900
x = 30
∴ AB = 2x = 60 cm. Answer: (3)

Ex.2 Area of the shaded region is
Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

(5) None of these

Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

Sol.

Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

Volume

Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

Length of a diagonal:

The length of diagonal of a cuboid = Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

The length of a diagonal of a cube = Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

Ex.1 An insect is crawling to climb a 20 metre long pipe of diameter 3.5 metres. If the insect take 4
circular rounds to reach the top of the building, then what will be total distance (in nearer
metres) traveled by insect to reach the top?
(1) 47 m

(2) 48 m

(3) 49 m

(4) 50 m

Sol. Since the insect is moving in circular way, so it will cover the distance which will be 4 times the distance
of the longest side AB of a right angled triangle. In the figure AO is equal to the circumference of the
pipe.
AO = πd = Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev = 11m
BO = 5 m
AB = = = 12.08 m
Total distance traveled = 12.08 × 4 = 48.32 m
Hence distance in nearer meters = 48 m

Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

Ex.2 The surface area of a cube is 726 sq metres. Find the volume of the cube.
(1) 1234 m²

(2) 1431 m²

(3) 1341 m

(4) 1331 m

(5) None of these

Sol. Surface area S = 726 m² Volume V = ?
In a cube,
S = 6a² = 726 ⇒ a² = 121 ⇒ a = 11 m
So, V = a³ = 11³ = 1331 m3. Answer: (4)

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